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# Trig 2640

### special angles and trig equations and identities

Question | Answer |
---|---|

Sin 0 | 0 |

Cos 0 | 1 |

Tan 0 | 0 |

Sin pi/6 | 1/2 |

Cos pi/4 | Square root of 2/2 |

Tan pi/6 | Square root of 3/3 |

Cos pi/6 | Square root of 3/2 |

Sin pi/4 | Square root of 2/2 |

Tan pi/4 | 1 |

Sin pi/3 | Square root of 3/2 |

Cos pi/3 | 1/2 |

Tan pi/3 | Square root 3 |

Sin pi/2 | 1 |

Cos pi/2 | 0 |

Tan pi/2 | Undefined |

Sum formula for Sin | SinACosB+CosASinB |

Sum formula for Cos | CosACosB-sinAsinB |

Sum formula for Tan | tanA+tanB/1-tanAtanB |

Difference Formula for sin | sin(A-B)= sinAcosB-cosAsinB |

Double angle formula for sin | sin(2A)= 2sinAcosA |

half-angle formula for sin | sin(A/2)= (+-)Square root of (1-cosA/2) |

tanA | sinA/cosA |

cotA | cosA/sinA |

Pythagorean identity 1 | sin^2(A) + cos^2(A) = 1 |

Law of sines | a/sinA = b/sinB = c/sinC |

Law of cosine | a^2 = b^2 + c^2 - 2bc cosA |

Parabola: formulas | Formulas: y^2 = 4px when parabola on x-axis x^2 = 4py when parabola on y-axis |

Ellipse: formula | formula: (x^2/a^2) + (y^2/b^2) = 1 |

Hyperbola: formulas | Formulas: (x^2/a^2) - (y^2/b^2) = 1 |

double angle formula for cos | cos(2A)= cos^2(A)-sin^2(A) |

double angle formula for tan | tan(2A)= 2tanA/1-tanA |

Difference Formulas for cos | cos(A-B)= cosAcosB+sinAsinB |

Difference Formulas for tan | tan(A-B)= tanA-tanB/1+tanAtanB |

half-angle formula for cos | cos(A/2)= square root of (1+cosA/2) |

half-angle formula for tan | tan(A/2)= square root of (1-cosA/1+cosA) |

Pythagorean identity 2 | tan^2(A) + 1 = sec^2(A) |

Pythagorean identity 3 | 1 + cot^2(A)= csc^2(A) |

Parabola: Foci | for when on x-axis (p,0) for when on y-axis (0,p) |

Ellipse: Foci | when a is bigger ((+-) square root of (a^2 - b^2), 0) when b is bigger (0, (+-) square root of (b^2 - a^2)) |

Hyperbola: Foci | When on x-axis, ((+-) square root of (a^2 + b^2), 0) When on y-axis, (0, (+-)square root of (b^2+a^2)) |

y = f(x) + c | Vertical shift c units up |

y = f(x) - c | Vertical shift c units down |

y = f(x + c) | Horizontal shift c units to the left |

y = f(x - c) | Horizontal shift c units to the right |

y = -f(x) | Reflection over x-axis |

y = f(-x) | Reflection over y-axis |

y = cf(x) | vertical stretch/shrink, when c > 1 it's stretch, (x,y)--> (x,y*c) |

y = f(cx) | horizontal stretch/shrink, c < 1 it's shrink, (x,y)--> (x*(1/c),y) |

a^0 = | 1 |

a^-n = | 1/a^n |

a^m(a^n) = | a^(m+n) |

a^m/a^n = | a^(m-n) |

(a^m)^n = | a^m*n |

(ab)^n = | (a^n)b^n |

log base a of 1 = | 0 |

log base a of a = | 1 |

log base a of a^n = | n |

a^log base a of x = | x |

log base a of (UV) = | log base a of U + log base a of V |

log base a of (u/v) = | log base a of u - log base a of v |

log base a of u^n = | n*log base a of U |

log base a of U = | log base b of U/ log base b of a |

Created by:
burtond